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804:. A molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy, which falls in the terahertz or infrared range. This forms the basis of infrared spectroscopy. Alternatively, the same vibrational excitation can be produced by an inelastic scattering process. This is called Stokes Raman scattering, by analogy with the
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In an optically anisotropic crystal, a light ray may have two modes of propagation with different polarizations and different indices of refraction. If energy may be transferred between these modes by a quadrupolar (Raman) resonance, phases remain coherent along the whole path, transfer of energy may
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In the original description of the inverse Raman effect, the authors discuss both absorption from a continuum of higher frequencies and absorption from a continuum of lower frequencies. They note that absorption from a continuum of lower frequencies will not be observed if the Raman frequency of the
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which corresponds to the energy of the exciting laser photons. Absorption of a photon excites the molecule to the imaginary state and re-emission leads to Raman or
Rayleigh scattering. In all three cases the final state has the same electronic energy as the initial state but is higher in vibrational
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Light may be pulsed, so that beats do not appear. In
Impulsive Stimulated Raman Scattering (ISRS), the length of the pulses must be shorter than all relevant time constants. Interference of Raman and incident lights is too short to allow beats, so that it produces a frequency shift roughly, in best
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In contrast to IR spectroscopy, where there is a requirement for a change in dipole moment for vibrational excitation to take place, Raman scattering requires a change in polarizability. A Raman transition from one state to another is allowed only if the molecular polarizability of those states is
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the intensity of Raman scattering when the analyzer is aligned with the polarization of the incident laser. When polarized light interacts with a molecule, it distorts the molecule which induces an equal and opposite effect in the plane-wave, causing it to be rotated by the difference between the
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A classical physics based model is able to account for Raman scattering and predicts an increase in the intensity which scales with the fourth-power of the light frequency. Light scattering by a molecule is associated with oscillations of an induced electric dipole. The oscillating electric field
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The different possibilities of light scattering: Rayleigh scattering (no exchange of energy: incident and scattered photons have the same energy), Stokes Raman scattering (atom or molecule absorbs energy: scattered photon has less energy than the incident photon) and anti-Stokes Raman scattering
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line. The frequency shifts are symmetric because they correspond to the energy difference between the same upper and lower resonant states. The intensities of the pairs of features will typically differ, though. They depend on the populations of the initial states of the material, which in turn
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employs the Raman effect for substances analysis. The spectrum of the Raman-scattered light depends on the molecular constituents present and their state, allowing the spectrum to be used for material identification and analysis. Raman spectroscopy is used to analyze a wide range of materials,
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energies. The initial Raman spectrum is built up with spontaneous emission and is amplified later on. At high pumping levels in long fibers, higher-order Raman spectra can be generated by using the Raman spectrum as a new starting point, thereby building a chain of new spectra with decreasing
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The elastic light scattering phenomena called
Rayleigh scattering, in which light retains its energy, was described in the 19th century. The intensity of Rayleigh scattering is about 10 to 10 compared to the intensity of the exciting source. In 1908, another form of elastic scattering, called
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published his work on the "Molecular
Diffraction of Light", the first of a series of investigations with his collaborators that ultimately led to his discovery (on 16 February 1928) of the radiation effect that bears his name. The Raman effect was first reported by Raman and his coworker
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can take place when some Stokes photons have previously been generated by spontaneous Raman scattering (and somehow forced to remain in the material), or when deliberately injecting Stokes photons ("signal light") together with the original light ("pump light"). In that case, the total
257:, and therefore color) as the incident photons, but different direction. Rayleigh scattering usually has an intensity in the range 0.1% to 0.01% relative to that of a radiation source. An even smaller fraction of the scattered photons (about 1 in a million) can be scattered
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amplitude. The disadvantage of intrinsic noise due to the initial spontaneous process can be overcome by seeding a spectrum at the beginning, or even using a feedback loop as in a resonator to stabilize the process. Since this technology easily fits into the fast evolving
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on 21 February 1928 (5 days after Raman and
Krishnan). In the former Soviet Union, Raman's contribution was always disputed; thus in Russian scientific literature the effect is usually referred to as "combination scattering" or "combinatory scattering". Raman received the
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and Raman activity which may assist in assigning peaks in Raman spectra. Light polarized in a single direction only gives access to some Raman–active modes, but rotating the polarization gives access to other modes. Each mode is separated according to its symmetry.
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component of electromagnetic radiation may bring about an induced dipole in a molecule which follows the alternating electric field which is modulated by the molecular vibrations. Oscillations at the external field frequency are therefore observed along with
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Raman-scattering rate is increased beyond that of spontaneous Raman scattering: pump photons are converted more rapidly into additional Stokes photons. The more Stokes photons that are already present, the faster more of them are added. Effectively, this
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only have two rotations because rotations along the bond axis do not change the positions of the atoms in the molecule. The remaining degrees of freedom correspond to molecular vibrational modes. These modes include stretching and bending motions of the
506:, and vibrational motion. Three of the degrees of freedom correspond to translational motion of the molecule as a whole (along each of the three spatial dimensions). Similarly, three degrees of freedom correspond to rotations of the molecule about the
422:
to record spectra. Early spectra took hours or even days to acquire due to weak light sources, poor sensitivity of the detectors and the weak Raman scattering cross-sections of most materials. The most common modern detectors are
1287:{\displaystyle {\frac {I_{\text{Stokes}}}{I_{\text{anti-Stokes}}}}={\frac {({\tilde {\nu }}_{0}-{\tilde {\nu }}_{M})^{4}}{({\tilde {\nu }}_{0}+{\tilde {\nu }}_{M})^{4}}}\exp \left({\frac {hc\,{\tilde {\nu }}_{M}}{k_{B}T}}\right)}
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field and there is demand for transversal coherent high-intensity light sources (i.e., broadband telecommunication, imaging applications), Raman amplification and spectrum generation might be widely used in the near-future.
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is a quantum number. Since the selection rules for Raman and infrared absorption generally dictate that only fundamental vibrations are observed, infrared excitation or Stokes Raman excitation results in an energy change of
498:. This number arises from the ability of each atom in a molecule to move in three dimensions. When dealing with molecules, it is more common to consider the movement of the molecule as a whole. Consequently, the 3
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Kosloff, Ronnie; Hammerich, Audrey Dell; Tannor, David (1992). "Excitation without demolition: Radiative excitation of ground-surface vibration by impulsive stimulated Raman scattering with damage control".
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energy in the case of Stokes Raman scattering, lower in the case of anti-Stokes Raman scattering or the same in the case of
Rayleigh scattering. Normally this is thought of in terms of wavenumbers, where
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In labs, femtosecond laser pulses must be used because the ISRS becomes very weak if the pulses are too long. Thus ISRS cannot be observed using nanosecond pulses making ordinary time-incoherent light.
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The Raman-scattering process as described above takes place spontaneously; i.e., in random time intervals, one of the many incoming photons is scattered by the material. This process is thus called
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1828:. In some circumstances, Stokes scattering can exceed anti-Stokes scattering; in these cases the continuum (on leaving the material) is observed to have an absorption line (a dip in intensity) at ν
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2555:. 75th Birthday of Christian Colliex, 85th Birthday of Archie Howie, and 75th Birthday of Hannes Lichte / PICO 2019 - Fifth Conference on Frontiers of Aberration Corrected Electron Microscopy.
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1960:: 'Rayleigh scattering of molecular nitrogen and oxygen in the atmosphere includes elastic scattering as well as the inelastic contribution from rotational Raman scattering in air').
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Itoh, Yuki; Hasegawa, Takeshi (2 May 2012). "Polarization
Dependence of Raman Scattering from a Thin Film Involving Optical Anisotropy Theorized for Molecular Orientation Analysis".
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The energy range for vibrations is in the range of approximately 5 to 3500 cm. The fraction of molecules occupying a given vibrational mode at a given temperature follows a
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is the rotational state. This generally is only relevant to molecules in the gas phase where the Raman linewidths are small enough for rotational transitions to be resolved.
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Raman scattering generally gives information about vibrations within a molecule. In the case of gases, information about rotational energy can also be gleaned. For solids,
1563:, which is the ratio of the Raman scattering with polarization orthogonal to the incident laser and the Raman scattering with the same polarization as the incident laser:
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to the incident photons, more commonly called a Raman shift. The locations of corresponding Stokes and anti-Stokes peaks form a symmetric pattern around the
Rayleigh
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different. For a vibration, this means that the derivative of the polarizability with respect to the normal coordinate associated to the vibration is non-zero:
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Weiner, A. M.; Wiederrecht, Gary P.; Nelson, Keith A.; Leaird, D. E. (1991). "Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy".
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Krivanek, O. L.; Dellby, N.; Hachtel, J. A.; Idrobo, J. -C.; Hotz, M. T.; Plotkin-Swing, B.; Bacon, N. J.; Bleloch, A. L.; Corbin, G. J. (1 August 2019).
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as an exciting light source. Because lasers were not available until more than three decades after the discovery of the effect, Raman and
Krishnan used a
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including gases, liquids, and solids. Highly complex materials such as biological organisms and human tissue can also be analyzed by Raman spectroscopy.
1879:, in which the frequencies of the two incident photons are equal and the emitted spectra are found in two bands separated from the incident light by the
261:, with the scattered photons having an energy different (usually lower) from those of the incident photons—these are Raman scattered photons. Because of
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Voehringer, Peter; Scherer, Norbert F. (1995). "Transient
Grating Optical Heterodyne Detected Impulsive Stimulated Raman Scattering in Simple Liquids".
402:
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A selection rule relevant only to ordered solid materials states that only phonons with zero phase angle can be observed by IR and Raman, except when
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Iliev, M. N.; Abrashev, M. V.; Laverdiere, J.; Jandi, S.; et al. (16 February 2006). "Distortion-dependent Raman spectra and mode mixing in RMnO
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rather than light. An increase in photon energy which leaves the molecule in a lower vibrational energy state is called anti-Stokes scattering.
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The effect is exploited by chemists and physicists to gain information about materials for a variety of purposes by performing various forms of
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is the intensity of Raman scattering when the analyzer is rotated 90 degrees with respect to the incident light's polarization axis, and
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The following focuses on the theory of normal (non-resonant, spontaneous, vibrational) Raman scattering of light by discrete molecules.
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is given for anti-Stokes. When the exciting laser energy corresponds to an actual electronic excitation of the molecule then the
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in 1923 and in older German-language literature it has been referred to as the Smekal-Raman-Effekt. In 1922, Indian physicist
2706:
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is used in atmospheric physics to measure the atmospheric extinction coefficient and the water vapour vertical distribution.
1761:. Generally, as the exciting frequency is not equal to the scattered Raman frequency, the corresponding relative wavelengths
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820:(now known to correspond to lower energy) than the absorbed incident light. Conceptually similar effects can be caused by
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222:, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves
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Jones, W. J.; Stoicheff, B. P. (30 November 1964). "Inverse Raman Spectra: Induced Absorption at Optical Frequencies".
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Dhar, Lisa; Rogers, John A.; Nelson, Keith A. (1994). "Time-resolved vibrational spectroscopy in the impulsive limit".
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723:{\displaystyle E_{n}=h\left(n+{1 \over 2}\right)\nu =h\left(n+{1 \over 2}\right){1 \over {2\pi }}{\sqrt {k \over m}}\!}
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For high-intensity continuous wave (CW) lasers, stimulated Raman scattering can be used to produce a broad bandwidth
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Stimulated Raman transitions are also widely used for manipulating a trapped ion's energy levels, and thus basis
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Light has a certain probability of being scattered by a material. When photons are scattered, most of them are
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Lamb, G. L. (1971). "Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium".
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1346:. In general, a normal mode is Raman active if it transforms with the same symmetry of the quadratic forms
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in recognition of its significance as a tool for analyzing the composition of liquids, gases, and solids.
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2360:"Raman Microspectroscopic Imaging of Binder Remnants in Historical Mortars Reveals Processing Conditions"
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Monitoring the polarization of the scattered photons is useful for understanding the connections between
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2989:"Live-Cell Bioorthogonal Chemical Imaging: Stimulated Raman Scattering Microscopy of Vibrational Probes"
1472:, which states that vibrational modes cannot be both IR and Raman active, applies to certain molecules.
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is conceptually similar but involves excitation of electronic, rather than vibrational, energy levels.
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Inaugural Address delivered to the South Indian Science Association on Friday, the 16th March, 1928
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1468:) are allowed according to the QHO. There are however many cases where overtones are observed. The
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is the wavenumber of the vibrational transition. Thus Stokes scattering gives a wavenumber of
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Wei, Lu; Hu, Fanghao; Chen, Zhixing; Shen, Yihui; Zhang, Luyuan; Min, Wei (16 August 2016).
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For solid materials, Raman scattering is used as a tool to detect high-frequency phonon and
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when anharmonicity is important. The vibrational energy levels according to the QHO are
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Schematic of a dispersive Raman spectroscopy setup in a 180° backscattering arrangement.
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The inverse Raman effect is a form of Raman scattering first noted by W. J. Jones and
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of the molecule's point group. As with IR spectroscopy, only fundamental excitations (
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for his discovery of Raman scattering. The effect had been predicted theoretically by
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The Raman effect is also involved in producing the appearance of the blue sky (see
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Molecular vibrational energy is known to be quantized and can be modeled using the
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orientation of the molecule and the angle of polarization of the light wave. If
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The specific selection rules state that the allowed rotational transitions are
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Raman spectroscopy has been used to chemically image small molecules, such as
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K. S. Krishnan; Raman, C. V. (1928). "The Negative Absorption of Radiation".
1964:
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Suppose that the distance between two points A and B of an exciting beam is
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of the molecule. For a linear molecule, the number of vibrational modes is 3
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the Stokes light in the presence of the pump light, which is exploited in
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284:, in addition to other possibilities. More complex techniques involving
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Singh, R. (2002). "C. V. Raman and the Discovery of the Raman Effect".
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24:
3054:. Graduate Texts in Physics (4 ed.). Springer. pp. 285–288.
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Everall, Neil J. (2002). "Raman Spectroscopy of the Condensed Phase".
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regarding molecular vibrations apply to Raman scattering although the
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and photomultiplier tubes were common prior to the adoption of CCDs.
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conditions, inversely proportional to the cube of the pulse length.
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degrees of freedom are partitioned into molecular translational,
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Prof. R. W. Wood Demonstrating the New "Raman Effect" in Physics
1911:
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resulting from the external field and normal mode vibrations.
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Rotating-polarization coherent anti-Stokes Raman spectroscopy
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Explanation from Hyperphysics in Astronomy section of gsu.edu
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1925:
1918:
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295:, who discovered it in 1928 with assistance from his student
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of scattering between two electrons by emission of a virtual
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material is vibrational in origin and if the material is in
1339:{\displaystyle {\frac {\partial \alpha }{\partial Q}}\neq 0}
791:{\displaystyle E=h\nu ={h \over {2\pi }}{\sqrt {k \over m}}}
410:
Modern Raman spectroscopy nearly always involves the use of
265:, the material either gains or loses energy in the process.
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495:
315:
2970:"Painless laser device could spot early signs of disease"
249:), such that the scattered photons have the same energy (
2357:
2116:
Smekal, A. (1923). "Zur Quantentheorie der Dispersion".
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Keresztury, Gábor (2002). "Raman Spectroscopy: Theory".
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The symmetry of a vibrational mode is deduced from the
964:{\displaystyle {\tilde {\nu }}_{0}-{\tilde {\nu }}_{M}}
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Scattering, absorption and radiative transfer (optics)
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1844:; the application of the phenomenon is referred to as
1798:
Several tricks may be used to get a larger amplitude:
977:
2468:
Weber, Alfons (2002). "Raman Spectroscopy of Gases".
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1875:. This process can also be seen as a special case of
1851:, and a record of the continuum is referred to as an
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The spectrum of the scattered photons is termed the
1022:{\textstyle {\tilde {\nu }}_{0}+{\tilde {\nu }}_{M}}
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A short description of spontaneous Raman scattering
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1706:
Stimulated Raman scattering and Raman amplification
335:The inelastic scattering of light was predicted by
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836:Raman scattering is conceptualized as involving a
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272:. Many other variants of Raman spectroscopy allow
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719:
365:in 1930 for his work on the scattering of light.
291:The Raman effect is named after Indian scientist
3359:
2784:
2723:"What is polarised Raman spectroscopy? - HORIBA"
1931:Raman spectroscopy can be used to determine the
2651:perovskites (R=La,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Y)".
2925:
2549:"Progress in ultrahigh energy resolution EELS"
1967:, in biological systems by a vibrational tag.
483:For any given molecule, there are a total of 3
3126:
2986:
2701:(4th ed.). McGraw–Hill. pp. 117–8.
2697:Banwell, Colin N.; McCash, Elaine M. (1994).
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276:to be examined, if gas samples are used, and
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1698:, then the vibrations at that frequency are
1603:{\displaystyle \rho ={\frac {I_{r}}{I_{u}}}}
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1425:{\displaystyle (x^{2},y^{2},z^{2},xy,xz,yz)}
288:, multiple laser beams and so on are known.
234:are shifted to lower energy. This is called
2742:Journal of the Optical Society of America B
1939:for molecules that do not have an infrared
1788:A crossing of the beams may limit the path
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1702:; meaning they are not totally symmetric.
479:Degrees of freedom (physics and chemistry)
461:modes may also be observed. The basics of
368:In 1998 the Raman effect was designated a
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3106:Raman Effect: fingerprinting the universe
3086:Raman Spectroscopy – Tutorial at Kosi.com
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1840:. This phenomenon is referred to as the
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386:Raman spectroscopy § Instrumentation
16:Inelastic scattering of photons by matter
2437:Raman spectroscopy for chemical analysis
2428:
2204:Raman, C. V. (1928). "A new radiation".
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1691:{\displaystyle \rho \geq {\frac {3}{4}}}
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3156:Coherent anti-Stokes Raman spectroscopy
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1983:Coherent anti-Stokes Raman spectroscopy
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2699:Fundamentals of Molecular Spectroscopy
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1899:Raman spectroscopy § Applications
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2498:Handbook of Vibrational Spectroscopy
2470:Handbook of Vibrational Spectroscopy
2401:
2392:
2093:Handbook of Vibrational Spectroscopy
1989:Coherent Raman Scattering Microscopy
3186:Surface-enhanced Raman spectroscopy
3176:Spatially offset Raman spectroscopy
2606:The Journal of Physical Chemistry A
2530:(Benjamin/Cummings 1982), pp.646-7
2439:. New York: John Wiley & Sons.
2358:Thomas Schmid; Petra Dariz (2019).
2042:Surface Enhanced Raman Spectroscopy
1769:are not equal. Thus, a phase-shift
906:{\displaystyle {\tilde {\nu }}_{M}}
877:is the wavenumber of the laser and
870:{\displaystyle {\tilde {\nu }}_{0}}
831:
370:National Historic Chemical Landmark
230:as incident photons from a visible
13:
3237:Stimulated Raman adiabatic passage
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2500:. Vol. 1. Chichester: Wiley.
2472:. Vol. 1. Chichester: Wiley.
2095:. Vol. 1. Chichester: Wiley.
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1443:
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14:
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2866:The Journal of Physical Chemistry
1743:Stimulated Raman scattering is a
1461:{\displaystyle \Delta \nu =\pm 1}
1432:, which can be verified from the
3332:
3321:
3320:
2005:List of surface analysis methods
816:in 1852, with light emission at
398:published by Raman and Krishnan.
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31:
3196:Transmission Raman spectroscopy
3191:Tip-enhanced Raman spectroscopy
3076:Raman Effect - Classical Theory
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2278:"C. V. Raman: The Raman Effect"
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1751:Requirement for space-coherence
838:virtual electronic energy level
2566:10.1016/j.ultramic.2018.12.006
2406:. John Wiley & Sons, Ltd.
2300:
2227:
2152:
2063:Harris and Bertolucci (1989).
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1500:{\displaystyle \Delta J=\pm 2}
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1066:depend on the temperature. In
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321:Molecular Diffraction of Light
236:normal Stokes-Raman scattering
1:
3300:Journal of Raman Spectroscopy
3181:Stimulated Raman spectroscopy
3048:Klingshirn, Claus F. (2012).
2993:Accounts of Chemical Research
2435:McCreery, Richard L. (2000).
2049:
1805:Optical parametric generation
1712:Stimulated Raman spectroscopy
299:. Raman was awarded the 1930
79:Light scattering by particles
3166:Resonance Raman spectroscopy
3005:10.1021/acs.accounts.6b00210
2031:Resonance Raman spectroscopy
1718:spontaneous Raman scattering
7:
2835:10.1103/PhysRevLett.69.2172
2161:"A review of the 1931 book
2159:Nature (19 December 1931).
1970:
1725:stimulated Raman scattering
599:quantum harmonic oscillator
593:Quantum harmonic oscillator
394:An early Raman spectrum of
10:
3394:
3378:Fiber-optic communications
2948:10.1103/PhysRevLett.13.657
2673:10.1103/physrevb.73.064302
1896:
1709:
1541:
590:
476:
450:
383:
310:
282:if an X-ray source is used
3316:
3291:
3245:
3204:
3148:
2893:Reviews of Modern Physics
2282:American Chemical Society
2206:Indian Journal of Physics
2065:Symmetry and Spectroscopy
1867:Supercontinuum generation
1538:Symmetry and polarization
1068:thermodynamic equilibrium
601:(QHO) approximation or a
434:
374:American Chemical Society
3307:Vibrational Spectroscopy
3278:Rule of mutual exclusion
2913:10.1103/RevModPhys.43.99
1470:rule of mutual exclusion
441:X-ray Raman spectroscopy
278:electronic energy levels
2928:Physical Review Letters
2815:Physical Review Letters
2402:Long, Derek A. (2002).
2377:10.3390/heritage2020102
2163:Der Smekal-Raman-Effekt
348:, and independently by
3161:Raman optical activity
2772:10.1364/JOSAB.8.001264
2236:Physics in Perspective
2067:. Dover Publications.
1853:inverse Raman spectrum
1775:(1/λ − 1/λ')
1692:
1658:
1631:
1604:
1521:
1501:
1462:
1426:
1340:
1288:
1050:
1023:
965:
907:
871:
802:Boltzmann distribution
792:
724:
560:
540:
520:
425:charge-coupled devices
407:
399:
324:
301:Nobel Prize in Physics
263:conservation of energy
2256:10.1007/s000160200002
1693:
1659:
1657:{\displaystyle I_{u}}
1632:
1630:{\displaystyle I_{r}}
1605:
1522:
1502:
1463:
1427:
1341:
1289:
1047:
1024:
966:
908:
872:
793:
725:
561:
541:
521:
405:
393:
318:
243:elastically scattered
134:X-ray crystallography
3253:Depolarization ratio
3095:Scientific American,
3051:Semiconductor Optics
2976:. 27 September 2010.
2526:and John H. Meiser,
2010:National Science Day
1995:Depolarization ratio
1978:Brillouin scattering
1842:inverse Raman effect
1820:Inverse Raman effect
1669:
1641:
1614:
1567:
1558:depolarization ratio
1544:Depolarization ratio
1511:
1479:
1440:
1350:
1307:
1077:
975:
917:
881:
845:
743:
612:
550:
530:
510:
447:Molecular vibrations
212:inelastic scattering
3273:Rayleigh scattering
3212:Raman amplification
2940:1964PhRvL..13..657J
2905:1971RvMP...43...99L
2878:10.1021/j100009a027
2827:1992PhRvL..69.2172K
2799:10.1021/cr00025a006
2754:1991JOSAB...8.1264W
2665:2006PhRvB..73f4302I
2618:2012JPCA..116.5560I
2321:1928Natur.122...12R
2248:2002PhP.....4..399S
2130:1923NW.....11..873S
2118:Naturwissenschaften
1958:Rayleigh Scattering
1947:Raman amplification
1941:absorption spectrum
1861:thermal equilibrium
1803:be large. It is an
1723:On the other hand,
463:infrared absorption
453:Molecular vibration
420:photographic plates
247:Rayleigh scattering
3142:Raman spectroscopy
2528:Physical Chemistry
2412:10.1002/0470845767
2288:on 12 January 2013
2138:10.1007/BF01576902
2026:Raman spectroscopy
1951:optical amplifiers
1904:Raman spectroscopy
1848:Raman spectroscopy
1826:Boris P. Stoicheff
1688:
1654:
1627:
1600:
1550:molecular symmetry
1532:phonon confinement
1517:
1497:
1458:
1422:
1336:
1284:
1051:
1019:
961:
903:
867:
788:
720:
587:Vibrational energy
556:
536:
516:
488:degrees of freedom
473:Degrees of freedom
408:
400:
325:
270:Raman spectroscopy
226:being gained by a
224:vibrational energy
94:Powder diffraction
3355:
3354:
2821:(15): 2172–2175.
2708:978-0-07-707976-5
2653:Physical Review B
2626:10.1021/jp301070a
2612:(23): 5560–5570.
2182:10.1038/1281026c0
2074:978-0-486-66144-5
1745:nonlinear optical
1686:
1598:
1520:{\displaystyle J}
1328:
1278:
1253:
1221:
1201:
1179:
1145:
1123:
1102:
1099:
1089:
1010:
988:
952:
930:
894:
858:
818:longer wavelength
786:
785:
774:
717:
716:
705:
685:
650:
559:{\displaystyle z}
539:{\displaystyle y}
519:{\displaystyle x}
494:is the number of
429:Photodiode arrays
354:Leonid Mandelstam
350:Grigory Landsberg
274:rotational energy
170:
169:
54:Bragg diffraction
3385:
3368:Raman scattering
3336:
3335:
3324:
3323:
3268:Raman scattering
3263:Nonlinear optics
3258:Four-wave mixing
3227:Raman microscope
3135:
3128:
3121:
3112:
3111:
3065:
3035:
3034:
3024:
2999:(8): 1494–1502.
2984:
2978:
2977:
2966:
2960:
2959:
2923:
2917:
2916:
2888:
2882:
2881:
2872:(9): 2684–2695.
2861:
2855:
2854:
2809:
2803:
2802:
2787:Chemical Reviews
2782:
2776:
2775:
2765:
2737:
2731:
2730:
2719:
2713:
2712:
2694:
2685:
2684:
2644:
2638:
2637:
2601:
2595:
2594:
2568:
2544:
2538:
2524:Keith J. Laidler
2521:
2512:
2511:
2493:
2484:
2483:
2465:
2459:
2458:
2432:
2426:
2425:
2404:The Raman Effect
2399:
2390:
2389:
2379:
2370:(2): 1662–1683.
2355:
2349:
2348:
2329:10.1038/122012b0
2304:
2298:
2297:
2295:
2293:
2284:. Archived from
2274:
2268:
2267:
2231:
2225:
2224:
2201:
2195:
2194:
2184:
2156:
2150:
2149:
2113:
2107:
2106:
2088:
2079:
2078:
2060:
2016:Nonlinear optics
1877:four-wave mixing
1793:
1783:
1776:
1771:Θ = 2π
1768:
1764:
1760:
1734:Raman amplifiers
1697:
1695:
1694:
1689:
1687:
1679:
1663:
1661:
1660:
1655:
1653:
1652:
1636:
1634:
1633:
1628:
1626:
1625:
1609:
1607:
1606:
1601:
1599:
1597:
1596:
1587:
1586:
1577:
1562:
1526:
1524:
1523:
1518:
1506:
1504:
1503:
1498:
1467:
1465:
1464:
1459:
1431:
1429:
1428:
1423:
1391:
1390:
1378:
1377:
1365:
1364:
1345:
1343:
1342:
1337:
1329:
1327:
1319:
1311:
1293:
1291:
1290:
1285:
1283:
1279:
1277:
1273:
1272:
1262:
1261:
1260:
1255:
1254:
1246:
1234:
1222:
1220:
1219:
1218:
1209:
1208:
1203:
1202:
1194:
1187:
1186:
1181:
1180:
1172:
1164:
1163:
1162:
1153:
1152:
1147:
1146:
1138:
1131:
1130:
1125:
1124:
1116:
1108:
1103:
1101:
1100:
1097:
1091:
1090:
1087:
1081:
1039:beat frequencies
1028:
1026:
1025:
1020:
1018:
1017:
1012:
1011:
1003:
996:
995:
990:
989:
981:
970:
968:
967:
962:
960:
959:
954:
953:
945:
938:
937:
932:
931:
923:
912:
910:
909:
904:
902:
901:
896:
895:
887:
876:
874:
873:
868:
866:
865:
860:
859:
851:
832:Raman scattering
797:
795:
794:
789:
787:
778:
777:
775:
773:
762:
729:
727:
726:
721:
718:
709:
708:
706:
704:
693:
691:
687:
686:
678:
656:
652:
651:
643:
624:
623:
603:Dunham expansion
582:
578:
568:Linear molecules
565:
563:
562:
557:
545:
543:
542:
537:
525:
523:
522:
517:
501:
493:
486:
332:was discovered.
280:may be examined
209:
208:
205:
204:
201:
198:
195:
192:
178:Raman scattering
162:
155:
148:
35:
21:
20:
3393:
3392:
3388:
3387:
3386:
3384:
3383:
3382:
3358:
3357:
3356:
3351:
3312:
3287:
3241:
3200:
3144:
3139:
3072:
3062:
3061:978-364228362-8
3044:
3042:Further reading
3039:
3038:
2985:
2981:
2968:
2967:
2963:
2934:(22): 657–659.
2924:
2920:
2889:
2885:
2862:
2858:
2810:
2806:
2783:
2779:
2763:10.1.1.474.7172
2738:
2734:
2721:
2720:
2716:
2709:
2695:
2688:
2650:
2645:
2641:
2602:
2598:
2553:Ultramicroscopy
2545:
2541:
2522:
2515:
2508:
2494:
2487:
2480:
2466:
2462:
2447:
2433:
2429:
2422:
2400:
2393:
2356:
2352:
2315:(3062): 12–13.
2305:
2301:
2291:
2289:
2276:
2275:
2271:
2232:
2228:
2202:
2198:
2157:
2153:
2124:(43): 873–875.
2114:
2110:
2103:
2089:
2082:
2075:
2061:
2057:
2052:
2047:
2000:Fiber amplifier
1973:
1901:
1895:
1869:
1839:
1833:
1822:
1789:
1778:
1770:
1766:
1762:
1756:
1753:
1714:
1708:
1678:
1670:
1667:
1666:
1648:
1644:
1642:
1639:
1638:
1621:
1617:
1615:
1612:
1611:
1592:
1588:
1582:
1578:
1576:
1568:
1565:
1564:
1560:
1546:
1540:
1512:
1509:
1508:
1480:
1477:
1476:
1441:
1438:
1437:
1434:character table
1386:
1382:
1373:
1369:
1360:
1356:
1351:
1348:
1347:
1320:
1312:
1310:
1308:
1305:
1304:
1300:
1298:Selection rules
1268:
1264:
1263:
1256:
1245:
1244:
1243:
1235:
1233:
1229:
1214:
1210:
1204:
1193:
1192:
1191:
1182:
1171:
1170:
1169:
1165:
1158:
1154:
1148:
1137:
1136:
1135:
1126:
1115:
1114:
1113:
1109:
1107:
1096:
1092:
1086:
1082:
1080:
1078:
1075:
1074:
1033:effect occurs.
1031:resonance Raman
1013:
1002:
1001:
1000:
991:
980:
979:
978:
976:
973:
972:
955:
944:
943:
942:
933:
922:
921:
920:
918:
915:
914:
897:
886:
885:
884:
882:
879:
878:
861:
850:
849:
848:
846:
843:
842:
834:
776:
766:
761:
744:
741:
740:
707:
697:
692:
677:
670:
666:
642:
635:
631:
619:
615:
613:
610:
609:
595:
589:
580:
576:
551:
548:
547:
531:
528:
527:
511:
508:
507:
499:
491:
484:
481:
475:
469:are different.
467:selection rules
455:
449:
437:
388:
382:
380:Instrumentation
313:
189:
185:
166:
46:
45:
39:Feynman diagram
17:
12:
11:
5:
3391:
3381:
3380:
3375:
3370:
3353:
3352:
3350:
3349:
3342:
3330:
3317:
3314:
3313:
3311:
3310:
3303:
3295:
3293:
3289:
3288:
3286:
3285:
3280:
3275:
3270:
3265:
3260:
3255:
3249:
3247:
3243:
3242:
3240:
3239:
3234:
3229:
3224:
3219:
3214:
3208:
3206:
3202:
3201:
3199:
3198:
3193:
3188:
3183:
3178:
3173:
3168:
3163:
3158:
3152:
3150:
3146:
3145:
3138:
3137:
3130:
3123:
3115:
3109:
3108:
3103:
3098:
3097:December 1930)
3088:
3083:
3078:
3071:
3070:External links
3068:
3067:
3066:
3060:
3043:
3040:
3037:
3036:
2979:
2961:
2918:
2883:
2856:
2804:
2793:(1): 157–193.
2777:
2732:
2727:www.horiba.com
2714:
2707:
2686:
2648:
2639:
2596:
2539:
2513:
2506:
2485:
2478:
2460:
2445:
2427:
2421:978-0471490289
2420:
2391:
2350:
2299:
2269:
2242:(4): 399–420.
2226:
2196:
2175:(3242): 1026.
2151:
2108:
2101:
2080:
2073:
2054:
2053:
2051:
2048:
2046:
2045:
2039:
2034:
2028:
2023:
2018:
2013:
2007:
2002:
1997:
1992:
1986:
1980:
1974:
1972:
1969:
1933:force constant
1897:Main article:
1894:
1891:
1873:supercontinuum
1868:
1865:
1835:
1829:
1821:
1818:
1813:
1812:
1808:
1796:
1795:
1752:
1749:
1710:Main article:
1707:
1704:
1685:
1682:
1677:
1674:
1651:
1647:
1624:
1620:
1595:
1591:
1585:
1581:
1575:
1572:
1542:Main article:
1539:
1536:
1516:
1496:
1493:
1490:
1487:
1484:
1457:
1454:
1451:
1448:
1445:
1421:
1418:
1415:
1412:
1409:
1406:
1403:
1400:
1397:
1394:
1389:
1385:
1381:
1376:
1372:
1368:
1363:
1359:
1355:
1335:
1332:
1326:
1323:
1318:
1315:
1299:
1296:
1295:
1294:
1282:
1276:
1271:
1267:
1259:
1252:
1249:
1241:
1238:
1232:
1228:
1225:
1217:
1213:
1207:
1200:
1197:
1190:
1185:
1178:
1175:
1168:
1161:
1157:
1151:
1144:
1141:
1134:
1129:
1122:
1119:
1112:
1106:
1095:
1085:
1055:Raman spectrum
1016:
1009:
1006:
999:
994:
987:
984:
958:
951:
948:
941:
936:
929:
926:
900:
893:
890:
864:
857:
854:
833:
830:
812:discovered by
784:
781:
772:
769:
765:
760:
757:
754:
751:
748:
732:
731:
715:
712:
703:
700:
696:
690:
684:
681:
676:
673:
669:
665:
662:
659:
655:
649:
646:
641:
638:
634:
630:
627:
622:
618:
591:Main article:
588:
585:
573:chemical bonds
555:
535:
515:
477:Main article:
474:
471:
451:Main article:
448:
445:
436:
433:
384:Main article:
381:
378:
346:K. S. Krishnan
330:Mie scattering
319:First page of
312:
309:
297:K. S. Krishnan
168:
167:
165:
164:
157:
150:
142:
139:
138:
137:
136:
131:
126:
121:
116:
111:
106:
101:
96:
91:
86:
81:
76:
71:
66:
61:
56:
48:
47:
37:
36:
28:
27:
15:
9:
6:
4:
3:
2:
3390:
3379:
3376:
3374:
3371:
3369:
3366:
3365:
3363:
3348:
3347:
3343:
3341:
3340:
3331:
3329:
3328:
3319:
3318:
3315:
3309:
3308:
3304:
3302:
3301:
3297:
3296:
3294:
3290:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3254:
3251:
3250:
3248:
3244:
3238:
3235:
3233:
3230:
3228:
3225:
3223:
3220:
3218:
3217:Raman cooling
3215:
3213:
3210:
3209:
3207:
3203:
3197:
3194:
3192:
3189:
3187:
3184:
3182:
3179:
3177:
3174:
3172:
3169:
3167:
3164:
3162:
3159:
3157:
3154:
3153:
3151:
3147:
3143:
3136:
3131:
3129:
3124:
3122:
3117:
3116:
3113:
3107:
3104:
3102:
3099:
3096:
3092:
3089:
3087:
3084:
3082:
3079:
3077:
3074:
3073:
3063:
3057:
3053:
3052:
3046:
3045:
3032:
3028:
3023:
3018:
3014:
3010:
3006:
3002:
2998:
2994:
2990:
2983:
2975:
2971:
2965:
2957:
2953:
2949:
2945:
2941:
2937:
2933:
2929:
2922:
2914:
2910:
2906:
2902:
2899:(2): 99–124.
2898:
2894:
2887:
2879:
2875:
2871:
2867:
2860:
2852:
2848:
2844:
2840:
2836:
2832:
2828:
2824:
2820:
2816:
2808:
2800:
2796:
2792:
2788:
2781:
2773:
2769:
2764:
2759:
2755:
2751:
2747:
2743:
2736:
2728:
2724:
2718:
2710:
2704:
2700:
2693:
2691:
2682:
2678:
2674:
2670:
2666:
2662:
2659:(6): 064302.
2658:
2654:
2643:
2635:
2631:
2627:
2623:
2619:
2615:
2611:
2607:
2600:
2592:
2588:
2584:
2580:
2576:
2572:
2567:
2562:
2558:
2554:
2550:
2543:
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1914:excitations.
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3283:Stokes shift
3267:
3205:Applications
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2021:Raman laser
1949:is used in
1937:bond length
1886:fiber laser
1700:depolarized
1098:anti-Stokes
363:Nobel Prize
341:C. V. Raman
293:C. V. Raman
129:Wolf effect
114:Small-angle
3362:Categories
3149:Techniques
2507:0471988472
2479:0471988472
2446:0471231878
2102:0471988472
2050:References
2037:Scattering
504:rotational
255:wavelength
109:Rutherford
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2758:CiteSeerX
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3292:Journals
3031:27486796
2974:BBC News
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2901:Bibcode
2823:Bibcode
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2244:Bibcode
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2126:Bibcode
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1767:λ'
566:-axes.
396:benzene
372:by the
311:History
216:photons
180:or the
174:physics
124:Thomson
119:Tyndall
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412:lasers
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